I still can't get my Apple ID to sign in so I can use iMessage or FaceTime

I have spent hours trying to get FaceTime and iMessage to work on my iPhone. I had no problems whatsoever with OS6, but as soon as I updated to os7.0.4 FaceTime and iMessage have become non-functional. I can't seem to sign in using an Apple ID.

Error message is "check network settings"

I have meticulously gone through troubleshooting steps in various articles to no avail. I have used 2 separate Apple ID's multiple wifi connections, restarted my phone, checked network settings, reset passwords, etc. I am at my wits end.